Nanomagnetic logic (NML), also known as, Magnetic Quantum-Dot Cellular Automata (MQCA) consists of using nanomagnetic islands arranged in such a way that allows logic functions to be performed by using NML circuits. Wires, gates, and inverters have already been demonstrated to function at room temperature. It is estimated that if 1010 magnets switch at 108 times/second, then the magnets would only dissipate about 0.1 W of power. These nanomagnet based devices can remain non-volatile provided that their size/shape remains above the superparamagnetic limit which means that these nanomagnets devices can be used to realize both logic and memory devices. If non-volatility can be sacrificed, research suggests that binary state in nanomagnets with feature sizes below the superparamagnetic limit should also be stable for around 1 millisecond. This retention time is sufficient to perform logic operations. Device switching times could also be reduced.
The fundamental building blocks for NML circuits can (i) be made with standard lithographic techniques and (ii) have all been experimentally demonstrated at room temperature. Wires that exhibit ferromagnetically ordering (FIG. 1a-c) can be formed by orienting rectangular magnets next to each other so that their magnetic poles are within a commonly shared axis as shown in the FIG. 1a-c. Likewise anti-ferromagnetically coupled bit wires can be formed by orienting rectangular magnets next to each other so that their magnetic poles are parallel to each other and not within a commonly shared axis as shown in FIG. 2a-c. 
Because the energy difference between magnetization (binary) states in an NML device can be hundreds of kT at room temperature, an applied magnetic clock is needed to facilitate the re-evaluation of an NML ensemble subsequent to when input states are changed. The applied magnetic clock provides the necessary energy that modulates the barrier between magnetization states so that fringing fields from individual magnets can quickly bias neighboring magnets into their respective thermodynamically favorable magnetization state that corresponds to the logically correct output states associated with the input(s). This reordering of magnetization states is guided by either antiferromagnetic or ferromagnetic coupling which is dependent upon the relative positions of how the particularly adjacent magnets are geometrically arranged.
For example, reordering of magnetization states in an antiferromagnetic coupled horizontal line would proceed as shown in FIG. 3-i to FIG. 3-iii (where just 3 devices are shown for simplicity). After the field of the left most magnet is externally driven by an Input (not shown) to flip its magnetic state, the applied magnetic clock field (H) is then subsequently imposed on all of the magnets (e.g., in an antiferromagnetically ordered line) which drives the internal magnetic fields (sideways arrows) of the center and right most magnets to be biased along their hard (shorter) axes (as shown in the transition from FIG. 3-i to FIG. 3-ii). Note that the internal magnetic field (up arrow) of the left most magnet is unaffected by the applied magnetic clock field (H) because it remains biased along its easy (long) axis driven by the continued imposition of the external magnetic field at the Input (not shown). As a result of imposing the applied magnetic clock field which drives the internal magnetic fields of the center and right most magnets pointed towards their hard axes (i.e., nullify), the energetic barriers of the center and right most magnets needed to reach their new energetically favorable magnetization state are considerably lowered. Flux from neighboring magnets can then efficiently bias these magnets into a new magnetically stable state (FIG. 3-iii) when the applied magnetic clock field (H) is removed.
It is known that fringing field-based interactions between single domain magnets with nanometer feature sizes can be used as a driving force to perform Boolean logic operations. With NML, logic functionality results from a complex interplay of shape anisotropy and magnet-to-magnet coupling. Magnet shape anisotropy, i.e., an elongated easy axis, creates a bi-stable system, and binary values (1/0) can be arbitrarily assigned to different magnetization directions. For many magnet shapes, the easy axis states are energetically equivalent for a magnet in isolation. When considering magnet ensembles, in clocked systems, fringing fields from individual devices can set the state of a neighboring device when that device is in a metastable logic state. It is known that these fringing field interactions can be used to implement majority voting gates and, in principle, implement any Boolean function.
To date, all known proposals for Boolean logic designs using NML architecture have either been majority gate based or assumed magnets with a uniform shape. Majority gates can be transformed into AND/OR or NAND/NOR gates and can be used to implement any Boolean function (as for AND/OR gates, inversion is possible with an antiferromagnetically ordered wire with an odd number of devices). One way of transforming a majority gate into either a AND/OR or NAND/NOR gate configuration is to permanently fix one of the inputs to a logic 0 or logic 1. Thus, Boolean logic can be realized using majority voting gates by arbitrarily setting one input of a majority gate to a logic ‘0’ or ‘1’, to transform the gate to a two input AND/OR gate. However, reducing a clocked majority gate to a 2-input AND/OR gate is non-trivial. The fixed/held input must be designed such that it does not impede the switching of the compute magnet (e.g., by providing too strong of a bias). If this does happen, a stuck-at fault will ensue as the two other inputs will not be able to drive the gate to a logically correct state.
Some advantages of NML designs include high scalability with ultra-low active power and essentially zero leakage power. NML are also thought to be inherently radiation resistant. To date, known NML designs have utilized elementary symmetrical shapes, i.e., rectangular and ellipsoid devices, have been used for majority gate logic designs.
As depicted in FIGS. 4-5, majority logic gates (MLG) have been used as a basis to demonstrate that magnetic quantum-dot cellular automata (MQCA) can be used to successfully implement various Boolean logic functions. Magnetic logic manipulates spin-polarized electrons in the magnetic material where information can be arbitrarily correlated with either “spin up” or “spin down” electrons. However, not all Boolean functions map well to majority voting gates (i.e. XOR). More specifically, an XOR gate constructed from majority gate-based AND/OR logic will likely require a relatively large footprint.
The same reference numerals refer to the same parts throughout the various figures.